Quantifying Luck in Head-to-Head Fantasy Leagues

If you've played fantasy football you know that success is somewhat dependent on luck.

Teams face off in head-to-head matchups and the higher scoring team wins (i.e., a team wins if it happens to be matched up against a lower scoring team during that particular week). If you post the second-highest score in your league during a particular week, you still lose if you are matched up against the highest scoring team. That's bad luck. Meanwhile, a low-scoring owner can luck out by facing an even worse owner.

Sports league scheduling is a dissertation unto itself (and a multi-billion dollar business when it comes to scheduling games for professional and college leagues) but in its simplest form, a fantasy league's schedule is a round-robin tournament among the owners. (Fleaflicker's scheduling algorithm is a bit more sophisticated, balancing inter- and intra-divisional matchups according to user specifications.)

During any given season, the ordering of the matchups is random. The schedule introduces an element of luck to an owner's win-loss record.

There are several ways to quantify this luck.

The brute-force approach is to enumerate all conceivable schedules for an owner and tally the results of each to yield a probability distribution for wins. For example, in a 12-team league in which each owner faces every other owner exactly once, there are 11! possible schedules for each team (this isn't entirely accurate--there are actually far fewer ways to schedule the league correctly for all teams--but from a single owner's perspective there are 11! possible schedules).

A less computationally-intensive approach is to compare each matchup's outcome to the probability of beating any owner in the league. For example, an owner who posts the league's lowest score has a 100% chance of losing that week--no luck is involved. An owner who posts the 2nd-lowest score of the week has a 1/11 chance of winning and a 10/11 chance of losing. If the owner lost, the owner was the victim of a tiny bit of bad luck. But a victory means the owner was the beneficiary of a lot of good luck.

(We added a luck column to your team schedule page so you can see this effect on your fantasy teams. Here is mine for a particularly lucky season.)

Can scheduling luck affect a fantasy owner's fortunes?

Across all 2008 Fleaflicker leagues, teams were involved in 3 luck games on average (games involving 50%+ luck as defined above).

Call a team lucky if it finished at least 2 games over .500 in luck matchups and unlucky if it finished at least 2 games under .500 in luck matchups. 20% of all teams last season were lucky and 20% were unlucky (so about 5 teams in a 12-team league were affected by luck).

Call a team good if it finished in the top-third of the league and bad if it finished in the bottom-third. 22% of good teams were lucky and 16% were unlucky while 18% of bad teams were lucky and 21% were unlucky.

Taking it one step further, call a team very lucky if it finished at least 3 games over .500 in luck matchups and very unlucky if it finished at least 3 games under .500 in luck matchups. 8% of all teams last season were very lucky and 8% were very unlucky.

10% of good teams were very lucky and 5% were very unlucky; 7% of the bad teams were very lucky and 9% were very unlucky.

Okay, after, obviously, losing my grasp of the English language with the last line of this post (It should have read: "It would have made understanding a lot easier") I hate to make mention of a grammatical error. But, when you roll your mouse over the Luck column header the last line reads: "that is bad very luck"

ok. wouldn't it be simpler to just allow everyone to play each team each week? will that be available for next year? please?

this year i'm not having fleaflicker track the standings for my league at all - i'm having everyone play everyone else and posting the standings on a google spreadsheet. and its by far the most enjoyable season my league has ever had.

in this post, you just stated how absolutely stupid the head-to-head system is. and yet, that is the only system that fleaflicker offers.

again, the best teams had 3.3 lucky wins and 2.4 unlucky losses. thats 5.7 luck based games - even assuming that you are talking about a full 17 week season, that means that 33.5% of the games are based on luck! (if you are talking about a 14 game regular season then its 40.7%) thats ridiculous!

after reading this post (fleafounder's, not mine), many people will say to themselves, "wow, the head-to-head system is really dumb". fleaflicker acknowledges this and even developed a luck-calculator to explain quite how dumb it really is. but still, it is the only system available.

Just to clarify, the "luck" is the difference between the winning probability and the losing probability based on the rank of points for a week?

Can we make scheduling luck a moot point by adding functionality where you play every team every week? For example, in a 12 team league where you have the 3rd best points scored in a week, your record for that week would be 9-2.

Double bump....I would love to see something like this....just having an all-play standings where you could see your record against every other team would be great. I've asked this before but never seem to get a response from flea flicker.

after 4 (or maybe 5? i've lost count) years of waiting, i have come to the conclusion that this is never gonna happen. the past few years i've been keeping play-all standings on a separate google spreadsheet, and completely clear the schedule so that noone ever plays everybody so no standings are kept on fleaflicker. it's a little bit of work but compared to the total amount of time spent on fantasy football it's really not such a big deal.

i don't know why fantasy football sites don't implement this. if fleaflicker would, they would be the only site that has this.

after last season i did this experiment: i took all of the actual scores from my league and applied them to a random fantasy football schedule generator, and then calculated the standings based on that.

then i found a different schedule generator, and took the SAME SCORES, (the actual scores from my league, applied them to THAT schedule, and determined the standings.

To reiterate.....I changed NOTHING except for the schedule. All of the scores were exactly the same. And of course, the standings came out completely differently. As far as I remember, maybe 3 or 4 teams finished with the same record. One team finished with a 4-game difference in wins!

The conclusions are obvious: 1) I am a geek, and 2)head-to-head is beyond stupid.